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An induced subgraph is a subgraph obtained from an original graph by removing a subset of vertices and/or edges together with any edges whose endpoints are both in this ...

A discrete subset of R^s which is closed under addition and subtraction and which contains Z^s as a subset.

A relation between permutations p and q that exists if there is a sequence of transpositions such that each transposition increases the number of inversions (Stanton and ...

The number of elements greater than i to the left of i in a permutation gives the ith element of the inversion vector (Skiena 1990, p. 27).

The maximum flow between vertices v_i and v_j in a graph G is exactly the weight of the smallest set of edges to disconnect G with v_i and v_j in different components (Ford ...

For an infinite population with mean mu, variance sigma^2, skewness gamma_1, and kurtosis excess gamma_2, the corresponding quantities for the distribution of means are ...

A set-like object in which order is ignored, but multiplicity is explicitly significant. Therefore, multisets {1,2,3} and {2,1,3} are equivalent, but {1,1,2,3} and {1,2,3} ...

A data structure designed to allow repeated extraction of the smallest remaining key (Skiena 1990, p. 38).

A random composition of a number n in k parts is one of the (n+k-1; n) possible compositions of n, where (n; k) is a binomial coefficient. A random composition can be given ...

A random partition of a number n is one of the P(n) possible partitions of n, where P(n) is the partition function P. A random partition can be given by RandomPartition[n] in ...